Off the top of my head:
Padres - Just missed the playoffs are recently as two years ago. NL West appears to lack a dominate team for now.
Pirates - Rumor is they're slowly headed in the right direction. NL Central doesn't appear to be terribly strong in the near future.
Mets - Now that Wilpon's Madoff issues have been resolved he can get back to worrying about the Mets. In the meantime the rest of the division has passed them by though.
Athletics - I don't see them doing anything beyond trying to be competitive for cheap until their stadium situation is resolved.
Mariners - They have some nice young players and have shown a willingness to spend money in the past.
Royals - I thought this was their year? Or is it next year? I can't keep up.
Twins - Bottoming out.
Orioles - Since it's impossible to make the playoffs finishing fifth in a division, it's going to be awhile.
Astros - They're a long way from the playoffs, and moving to the AL isn't going to help matters.
I think the Mariners are the best team on the list. They have to battle with the Rangers and Angles though. I know it's possible for three teams from one division to make the playoffs, but that seems unlikely.
It comes down to the Padres, Pirates, and, maybe, the Royals to me. I have no faith in the Pirates or Royals so I'll vote for the Padres.
My 2012 White Sox record: 3-1
4/13 - Sox 5, Tigers 2
6/7 - Sox 4, Blue Jays 3
6/23 - Sox 8, Brewers 6
8/8 - Sox 1, Royals 2